But tuna doesn't show the whole call tree!

Right, and that's because the whole timed call tree cannot be retrieved from profile
data. Python developers made the decision to only store parent data in profiles
because it can be computed with little overhead.
To illustrate, consider the following program.

The root process (__main__) calls a() which spends 4 seconds in c() and 1 second
in d(). __main__ also calls b() which calls a(), this time spending 1 second in
c() and 4 seconds in d(). The profile, however, will only store that c() spent a
total of 5 seconds when called from a(), and likewise d(). The information that the
program spent more time in c() when called in root -> a() -> c() than when called in
root -> b() -> a() -> c() is not present in the profile.

tuna only displays the part of the timed call tree that can be deduced from the profile: